I searched the Irish Family History Foundation's database. It contains 11,500,000 survivng rcds for abt 60% of Irish counties. Rcds B4 1840 are sparse. My search focused on Co. Louth.
I am a bit perplexed on your posted data. 1. Generally, birth registrations list the parents' names, and sometimes the mother's maiden name. 2. Census data, if from the right decade, will list the parent's and children's names, and record where they were born. 3. Death certificates often list the age at death, or DOB. In any case, the date of death triggers the family to give obit data to the local newspaper(s). Obits are gold mines of info.
Now for searching Irish data. The IFHF database has roughly 1,000 B & M rcds for the surname Kerley (+variants). In this total, 290 Kirely B rcds are for Co. Louth between 1700 and 1921. Of these, 140 were rcd'd in the parish of Dundalk. The forenames of Constantine, John, Thomas and James are well represented.
For Arthur's Uncle, Constantine KERLEY, B abt 1835 +/- 4 yrs, there appear to be birth rcds for this man, and possibly his father in 1797, in Dundalk parish.
For Maria KERLEY (+variants) D 1882, she appears to have been born in the U.S. as there are NO B rcds for her in either Co. Louth, or Ireland, prior to 1892.
For Bridget KERLEY (+variants) D 1872, there are 13 relevant B rcds in Louth, 8 of which are in Dundalk.
For Ann KERLEY (+variants) D 1885, there are 18 B rcds in Louth, 10 of which are in Dundalk.
Obits for the above SHOULD name the spouse, DOB, DOM, offspring, etc. From this, you could get B and M certs.
Google the Foundation's name to lead you to this database.